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We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component,…

Disordered Systems and Neural Networks · Physics 2014-11-18 Ginestra Bianconi , Sergey N. Dorogovtsev

The behavior of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable to…

Physics and Society · Physics 2010-07-06 B. Berche , C. von Ferber , T. Holovatch , Yu. Holovatch

Robust and efficient design of networks on a realistic geographical space is one of the important issues for the realization of dependable communication systems. In this paper, based on a percolation theory and a geometric graph property,…

Data Analysis, Statistics and Probability · Physics 2011-11-04 Yukio Hayashi

We explore the robustness of complex networks against physical damage. We focus on spatially embedded network models and datasets where links are physical objects or physically transfer some quantity, which can be disrupted at any point…

Statistical Mechanics · Physics 2024-12-13 Luka Blagojević , Ivan Bonamassa , Márton Pósfai

The study of network robustness is a critical tool in the characterization and sense making of complex interconnected systems such as infrastructure, communication and social networks. While significant research has been conducted in all of…

Social and Information Networks · Computer Science 2022-03-31 Scott Freitas , Diyi Yang , Srijan Kumar , Hanghang Tong , Duen Horng Chau

Network robustness is an essential system property to sustain functionality in the face of failures or targeted attacks. Currently, only the connectivity of the nodes unaffected by an attack is utilized to assess robustness. We propose to…

Physics and Society · Physics 2023-01-18 Marcus Engsig , Alejandro Tejedor , Yamir Moreno

Infrastructure systems, such as power, transportation, telecommunication, and water systems, are composed of multiple components which are interconnected and interdependent to produce and distribute essential goods and services. So, the…

Physics and Society · Physics 2021-10-14 Zahra Mahabadi , Liz Varga , Tom Dolan

Real networks are vulnerable to random failures and malicious attacks. However, when a node is harmed or damaged, it may remain partially functional, which helps to maintain the overall network structure and functionality. In this paper, we…

Physics and Society · Physics 2022-03-14 L. D. Valdez , L. A. Braunstein

We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and…

Disordered Systems and Neural Networks · Physics 2009-11-07 Petter Holme , Beom Jun Kim , Chang No Yoon , Seung Kee Han

We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…

Statistical Mechanics · Physics 2014-11-20 Brian Karrer , M. E. J. Newman , Lenka Zdeborová

We study the robustness properties of multiplex networks consisting of multiple layers of distinct types of links, focusing on the role of correlations between degrees of a node in different layers. We use generating function formalism to…

Physics and Society · Physics 2014-05-02 Byungjoon Min , Su Do Yi , Kyu-Min Lee , K. -I. Goh

The behaviour of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable…

Physics and Society · Physics 2012-09-25 Bertrand Berche , Christian von Ferber , Taras Holovatch , Yurij Holovatch

Recently much attention has been paid to the study of the robustness of interdependent and multiplex networks and, in particular, networks of networks. The robustness of interdependent networks can be evaluated by the size of a mutually…

Statistical Mechanics · Physics 2015-06-18 Ginestra Bianconi , Sergey N. Dorogovtsev

In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], the authors proposed a simple measure for network robustness under malicious attacks on nodes. With a greedy algorithm, they found the optimal structure with respect to this…

Physics and Society · Physics 2012-06-28 An Zeng , Weiping Liu

Most real-world complex systems can be modelled by coupled networks with multiple layers. How and to what extent the pattern of couplings between network layers may influence the interlaced structure and function of coupled networks are not…

Data Analysis, Statistics and Probability · Physics 2010-10-26 Won-kuk Cho , K. -I. Goh , I. -M. Kim

Thanks to their extensive capacity, over-parameterized neural networks exhibit superior predictive capabilities and generalization. However, having a large parameter space is considered one of the main suspects of the neural networks'…

The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…

Physics and Society · Physics 2021-01-27 Peter Mann , V. Anne Smith , John B. O. Mitchell , Simon Dobson

We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, the strategies for enhancing robustness and immunization of a…

Physics and Society · Physics 2009-09-29 Liang Huang , Lei Yang , Kongqing Yang

In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of…

Physics and Society · Physics 2014-02-27 Dharshana Kasthurirathna , Mahendra Piraveenan , Gnanakumar Thedchanamoorthy

Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…

Physics and Society · Physics 2025-09-30 Jessica Jiang , Allison C. Zhuang , Petter Holme , Peter J. Mucha , Alice C. Schwarze